Higher-Order Least Squares: Assessing Partial Goodness of Fit of Linear Causal Models

Christoph Schultheiss, Peter Bühlmann and Ming Yuan

Journal of the American Statistical Association, 2024, vol. 119, issue 546, 1019-1031

Abstract: We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings. Supplementary materials for this article are available online.

Date: 2024
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DOI: 10.1080/01621459.2022.2157728

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